Unification of Forces

Unification

When the complications of charge and mass are removed from force equations, and substituted with a dimensionless count of particles (Q), it can be shown that all force equations are related to the electric force.  These equations are summarized in classical format related to the electron’s energy and radius (E_e and r_e), in addition to coupling constants (α) explained on this page as a ratio of geometries when wave form changes. The equations are validated on their respective force pages: electric, gravitational, magnetic, strong and orbital. The weak force is excluded, as explained on a separate page.

Note that the magnetic force of electromagnetism described here is based on a flow of electrons, which is differentiated from a static magnet, described in more detail here. Therefore, it is based on velocity (v). The remainder of the forces require coupling constants, which is the strength of the force relative to the electric force. These forces are based on geometric ratios as waves change in type or form.

Forces Summary

A summary of the forces and the simple version of the equation using classical forms with the electron’s energy, mass and radius (E_e, m_e and r_e) is found below.  The wave constant form can be derived from these equations. The forces in the following sections are all derived from these descriptions and classical equations.

Coupling Constants and their Geometry Ratio

In the Geometry of Spacetime, all coupling constants are modeled as a ratio of the geometric shapes for transverse and longitudinal waves. A unit cell of the lattice structure of spacetime is shown below in (1).  The wave center (blue) is in motion in (2) passing through a surface area best described by a rectangular geometry.  As it reaches its maximum displacement in (3) it returns to equilibrium.  After returning to equilibrium in (4) it has transferred its energy to granules in the lattice that continue to spread spherically.  The direction of initial motion is also represented by a cone as it propagates outwards from the center. This motion creates two surface areas that will be measured for energy: the surface area of a rectangle, and the surface area of the combination of a sphere and cone.

Vibration of Center Granule – Rectangle vs Sphere+Cone Surface Areas

Next, this is put into equation format. A plane wave passing through a surface area (S_r) of a rectangle with length (x) and width (y) is shown below.  A spherical wave with a component that flows from the center in a conical shape with slant length (l) and radius (d) is also shown below as surface area S_s.  This represents the change in wave type from transverse to spherical or vice versa in wave geometry.

The ratio of S_r to S_s is expressed in equation format with the surface area of a rectangle (x * y), the surface area of a sphere (4 * π * l²) and the surface area of a cone (π * d * l + π * d²).

Coupling Constant Geometry Ratio

Strong, Gravitational and Orbital Forces – Geometry

With the exception of the magnetic force, which is based on electron velocity, the remaining forces that require coupling constants are based on a single geometric ratio. Using the electric force as the baseline, the coupling constants relative to the electric force can be summarized as:

Strong Force (x=r_e ; y=r_e ; d=r_e ; l=π*r_e)

All variables from the coupling constant geometry ratio equation (above) are set to the electron’s radius (r_e).  This becomes the coupling constant for the strong force, known as the fine structure constant (α or α_e). It becomes stronger than the electric force as it utilizes all in-wave energy, compared with the electric force of the electron which utilizes in-wave energy to become both electric (longitudinal) and magnetic (transverse) as a result of particle spin.  Note the strong force is the inverse of the fine structure constant relative to the electric force.

Gravitational Force (Electron) (x=l_P ; y=l_P ; d=r_e ; l=π*r_e)

The variables for the sides of the rectangle from the coupling constant geometry ratio equation (above) are set to Planck length (l_P) and the cone radius and slant length are set to the electron’s radius (r_e). This matches the results for the electron’s gravitational coupling, which is the force of gravity between two electrons. The proton has its own gravitational coupling constant, which can be used for the calculation of gravity for large bodies.  The proton’s coupling constant can be derived from the electron’s constant multiplied by the square of the proton-electron mass ratio.

Orbital Force (x=r ; y=r_e ; d=r_e ; l=π*r_e)

The same variables as the fine structure are used for the coupling constant geometry ratio equation (above), with the exception of the width (x) for the rectangle.  It is now a variable distance (r) as the electron’s distance from a nucleus will vary based on the atomic element. Thus, it cannot be solved directly – the use of the equation is found in calculations in the Atomic Orbitals paper where radius is known for each element and seen on this site in the equations for atoms. When substituted into the equation for atoms, the fine structure constant is now squared (α_e²) and the radius distance is now cubed (r³), which is the behavior seen in permanent magnets.

It is labeled as α_Me as it is a force that not only keeps electrons in orbit, as explained here, but also for the static magnetic force seen in permanent magnets (not to be confused with the magnetic force from electromagnetism based on electron velocity).